Question

How many different strings can be formed by rearranging the letters in the word DCDCD?

Answer 1

Answer:

The different strings which can be formed by rearranging the letters in the word DCDCD are:

                                     10

Step-by-step explanation:

We are asked to find the different number of arrangements that may be me made in the word:

                               DCDCD

There are a total of 5 words such that D is repeated 3 times and C is repeated two times.

Hence, the total number of ways of arrangement is given by:

$=\dfrac{5!}{3!\times 2!}\\\\=\dfrac{5\times 4\times 3!}{3!\times 2!}\\\\=\dfrac{5\times 4}{2!}\\\\=\dfrac{5\times 4}{2}\\\\=10$

Hence, the total number of ways are:  10